# Without solving, how do you determine the number of solutions for the equation #sectheta=(2sqrt3)/3# in #-180^circ<=theta<=180^circ#?

##### 1 Answer

#### Answer:

Two solutions.

See explanation.

#### Explanation:

So you're really looking at where

Since the cosine function is "even",

So if there is a solution from 0 to

We can readily see that

because

We know that the range of the cosine function is between -1 and 1, so this is good news, this means that there is a solution (if the value was larger than 1, we would have had zero solution).

Therefore,

Thus,

Q.E.D.